Sensor Selection for Event Detection in Wireless Sensor Networks

Abstract

We consider the problem of sensor selection for event detection in wireless sensor networks (WSNs).We want to choose a subset of p out of n sensors that yields the best detection performance. As the sensor selection optimality criteria, we propose the Kullback-Leibler and Chernoff distances between the distributions of the selected measurements under the two hypothesis. We formulate the maxmin robust sensor selection problem to cope with the uncertainties in distribution means. We prove that the sensor selection problem is NP hard, for both Kullback-Leibler and Chernoff criteria. To (sub)optimally solve the sensor selection problem, we propose an algorithm of affordable complexity. Extensive numerical simulations on moderate size problem instances (when the optimum by exhaustive search is feasible to compute) demonstrate the algorithm's near optimality in a very large portion of problem instances. For larger problems, extensive simulations demonstrate that our algorithm outperforms random searches, once an upper bound on computational time is set. We corroborate numerically the validity of the KullbackLeibler and Chernoff sensor selection criteria, by showing that they lead to sensor selections nearly optimal both in the Neyman-Pearson and Bayes sense.

Sensor selection for estimation, filtering, and detection

“…Therefore, a weaker performance criterion which is easier to evaluate and optimize is often used. The relative entropy or the Kullback-Leibler (KL) distance is a frequently used performance criterion for design problems related to hypothesis testing [15], [22]. The sensor selection problem in [15] is formulated as the design of a selection matrix which is a non-convex optimization problem (even after appropriate relaxation).…”

“…The relative entropy or the Kullback-Leibler (KL) distance is a frequently used performance criterion for design problems related to hypothesis testing [15], [22]. The sensor selection problem in [15] is formulated as the design of a selection matrix which is a non-convex optimization problem (even after appropriate relaxation). However, similar to the sensor selection framework developed for estimation and filtering in Section III, we can also formulate sensor selection for hypothesis testing problems.…”

“…The purpose of this partly tutorial paper is to describe the sensor selection problem from a statistical signal processing perspective, and to provide a brief overview with a specific emphasis on some recent advances based on results from [12]- [15].…”

Sparse sensing for distributed gaussian detection

“…The central question of interest, i.e., sensing design for Gaussian detection problems, has been studied in the past [2,3]. In [2], this This work was supported in part by STW under FASTCOM project (10551) and in part by NWO-STW under the VICI program (10382).…”

“…Similarly, the formulation in [3] results in a complex non-convex (even after appropriate relaxations) solver on the Stiefel manifold. Different from [2,3], the proposed formulation leads to an elegant convex optimization solver.…”